CSEC Mathematics Workshop SBA
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1. The document determines the maximum dimensions of a corn farm that a farmer can fence using 100 meters of wire. The largest area is 625 square meters which occurs when the length and width are both 25 meters, making the field a square. 2. Using recommended spacing of corn seedlings, the document calculates the farmer can plant 4592 seedlings in the 625 square meter field by planting them in 28 rows with 164 seedlings in each row. 3. The calculations allow the farmer to utilize the maximum space available and determine the optimal number of seedlings to plant.
CSEC Mathematics Workshop SBA
- 1. 1 MATHEMATICS SCHOOL BASED ASSESMENT DETERMINING THE DIMENSIONS OF A CORN FARM TO GIVE MAXIMUM USE OF SPACE
- 2. 2 TABLE OF CONTENTS TITLE PAGE Acknowledgement………………………………………………………………………………………...3 Title of Project……………………………………………………………………………………………….4 Purpose of Project…………………………………………………………………………………………4 Problem Statement …….………………………………………………………………………………..5 Problem Formulation …………………..……………………………………………………………….6 Data Analysis ……………..…………………………………………………………………………………7 Problem Calculation and Analysis …….…………………………………………………………..8 Discussion of Findings .…………….……………………………..…………………………………….9 Conclusion …………………………….………………………………………………………………………9 Bibliography …………………………………………………………………………………………………10
- 3. 3 ACKNOWLEDGEMENT I would like to express my special thanks to all the persons who helped me with this project. Thank you all for your continuous help and support.
- 4. 4 TITLE OF PROJECT Determining the maximum dimensions of a corn farm and the number of seedlings that can be planted on it. INTRODUCTION PURPOSE OF STUDY The purpose of the project is to determine the dimensions that will give maximum space for the amount of wire that a farmer has available. My neighbor, Farmer Joe was given two rolls of wire by the Rural Agricultural Development Authority (RADA) Foundation. This is in aid of helping him to put up a fencing for the corn he wanted to invest in. Each roll of wire is 50 metres long. Mr. Joe has sought my assistance with the calculations for the maximum space that he can enclose with his 100 metres of wire and the number of corn seedlings that he can plant. He wants a rectangular farm for his corn, and he wants to utilize as much space as possible. Problem Solution 1 roll of wire = 50 metre 2 rolls of wire = 2 x 50 = 100 m Mr. Joe has 100 metres of wire available.
- 5. 5 The perimeter of wire that the farmer has amounts to 100 metres. Efforts were made to get the dimensions that would give a rectangle so that the largest area can be found. It was decided to start with the smallest unit of one on both widths of a rectangle as shown. The table was constructed starting with the width of 1m, then doing the calculations to get the length. Width Length Area 1 m 100 – (1 + 1) = 98, 48 ÷ 2 = 49 49 49 x 1 = 49 2 m 100 – (2 + 2) = 96, 96 ÷ 2 = 48 48 48 x 2 = 99 1m 24m 24m 1m
- 6. 6 Problem Calculation Perimeter = 100 metres Width Calculations Length Area 1 m 100 – (1 + 1) = 98, 98 ÷ 2 = 49 49 49 x 1 = 49 2 m 100 – (2 + 2) = 96, 96 ÷ 2 = 48 48 48 x 2 = 99 3 m 100 – (3 + 3) = 94, 94 ÷ 2 = 47 47 47 x 3 = 141 4 m 100 – (4 + 4) = 92, 92 ÷ 2 = 46 46 46 x 4 = 184 5 m 100 – (5 + 5) = 90, 90 ÷ 2 = 45 45 45 x 5 = 225 6 m 100 – (6 + 6) = 88, 88 ÷ 2 = 44 44 44 x 6 = 264 7 m 100 – (7 + 7) = 86, 86 ÷ 2 = 43 43 43 x 7 = 301 8 m 100 – (8 + 8) = 84, 84 ÷ 2 = 42 42 42 x 8 = 336 9 m 100 – (9 + 9) = 82, 82 ÷ 2 = 41 41 41 x 9 = 369 10 m 100 – (10 + 10) = 80, 80 ÷ 2 = 40 40 40 x 10 = 400 11 m 100 – (11 + 11) = 78, 78 ÷ 2 = 39 39 39 x 11 = 429 12 m 100 – (12 + 12) = 76, 76 ÷ 2 = 38 38 38 x 12 = 456 13 m 100 – (13 + 13) = 74, 74 ÷ 2 = 37 37 37 x 13 = 481 14 m 100 – (14 + 14) = 72, 72 ÷ 2 = 36 36 36 x 14 = 504 15 m 100 – (15 + 15) = 70, 70 ÷ 2 = 35 35 35 x 15 = 525 16 m 100 – (16 + 16) = 68, 68 ÷ 2 = 34 34 34 x 16 = 544 17 m 100 – (17 + 17) = 66, 66 ÷ 2 = 33 33 33 x 17 = 561 18 m 100 – (18 + 18) = 64, 64 ÷ 2 = 32 32 32 x 18 = 576 19 m 100 – (19 + 19) = 62, 62 ÷ 2 = 31 31 31 x 19 = 589 20 m 100 – (20 + 20) = 60, 60 ÷ 2 = 30 30 30 x 20 = 600 21 m 100 – (21 + 21) = 58, 58 ÷ 2 = 29 29 29 x 21 = 609 22 m 100 – (22 + 22) = 56, 56 ÷ 2 = 28 28 28 x 22 = 616 23 m 100 – (23 + 23) = 54, 54 ÷ 2 = 27 27 27 x 23 = 621 24 m 100 – (24 + 24) = 52, 52 ÷ 2 = 26 26 26 x 24 = 624 25 m 100 – (25 + 25) = 50, 50 ÷ 𝟐 = 25 25 25 x 25 = 625 26 m 100 – (26 + 26) = 48, 48 ÷ 2 = 24 24 24 x 26 = 624 27 m 100 – (27 + 27) = 46, 46 ÷ 2 = 23 23 23 x 27 = 621 28 m 100 – (28 + 28) = 44, 44 ÷ 2 = 22 22 22 x 28 = 616
- 7. 7 The lengths and the widths were then used to find the area, and the highest value observed. DATA ANALYSIS The calculations above have shown that the largest area that can be enclosed with the 100 metres of wire will be 625m2 . This was had when the length of the rectangle is 10 m and width is 10 m. With the length and the width being equal, the polygon is a square. Since the square is a rectangle, Mr. Joe will have his rectangular corn field. After the land is fenced with the largest possible area, the seedlings will be ready for planting. According to research, corn loves hot climate like Jamaica/Belize. It is said that the corns that grow in temperature greater than 65o C are the sweetest. To get the best crop of corn, experts say the seeds should be planted 1 inch deep and 4 to 6 inches 25 m 25 m
- 8. 8 apart. Rows should be 30 to 36 inches apart. Retrieved from: http://www.almanac.com/plant/corn. This will be used to guide the calculation for the number of seedlings Mr. Joe will invest in. Problem Calculation and Analysis With that specification, I will calculate the number of seedlings to plant in the 625m2 of land. 25 m = 984.25 inches; rounded to nearest whole number gives: 25 m = 984 inches Rows should be 30 to 36 inches apart according to the experts. Using 35 inches apart will give: 984. ÷ 35 = 28.1 It is therefore recommended that Mr. Joe has 28 rows, each being approximately 35 inches apart. Seedlings should be 4 to 6 inches apart, so using 6 inches gives length of row divide by 6. 984. ÷ 6 = 164 Each row has 164 seedlings. 28 rows x 164 = 4592 seedlings. 984 in 984 in
- 9. 9 Mr. Joe has space to plant 4592 seedlings on the plot of land that he has fenced. Rows should be 30 to 36 inches apart, and seedlings 4 to 6 inches apart in each row. If Farmer Joe follows the specification, the rows should be similar to the diagram above. DISCUSSION OF FINDINGS Finding the maximum area from a given perimeter can be done by writing out the lengths and the widths and taking their products. One may think that the large lengths would give the maximum area but this was not so. It works out that when the length and the width were equal, that is when the largest area occurred. In determining the number of seedlings, one must first ensure that the values being compared are of the same unit. The length was then divided to get the number of rows, and the length of a row divided to get the number of seedlings in each row. The total number of seedlings was derived by multiplying the number of rows by the number in each row. This calculation will assist the farmer in making the proper choice to get a good crop of corn. CONCLUSION The maximum area that can be had from a perimeter of 100m is 625m2 . This occurred from the length and the width being equal.
- 10. 10 The total number of seedlings to be planted on this plot of land, based on the recommended spacing of experts, is 4592.
- 11. 11 BIBLIOGRAPHY Sweet Corn: Planting, Growing and Harvesting Sweet Corn. Retrieved from http://www.almanac.com/plant/corn Toolsie, R. (1996). Mathematics: A Complete Course with C.X.C. Questions, San Fernando: Caribbean Educational Publishers.